Root (124) shared a stand of 179 with Moeen Ali (99no) as England reached stumps on 311 for four, after India’s spinners had briefly threatened to derail the tourists’ hopes of cashing in on winning the toss in Rajkot.
From 102 for three at lunch, the Yorkshireman continued to drive all the spinners well through the off-side - and picked up runs with the sweep too - as he and Moeen consigned India to a wicketless middle session and took some of the heat out of world number one bowler Ravi Ashwin’s fearsome reputation.
Root barely put a foot wrong until he drove a low catch straight back at Umesh Yadav in mid-evening and departed, after a third-umpire consultation which provided an additional talking point, to a fine-margin decision that the bowler had the ball under control before dropping it again in a faulty celebratory juggle.
It was imperative England took advantage of batting first, and they needed some early fortune to scramble a foothold as openers Alastair Cook and Haseeb Hameed benefited from dropped chances - only for Ravindra Jadeja and Ashwin to intervene before lunch.
Cook soon found he was struggling to attune himself on a pitch surprisingly dappled with green and providing some carry for India’s new-ball seamers.
His start was alarmingly scratchy, dropped on nought and one - at gully by Ajinkya Rahane when Mohammed Shami went round the wicket in the first over and then at second slip by Virat Kohli off Yadav.
Teenage debutant Hameed, Cook’s 10th opening partner since the retirement of Andrew Strauss four years ago, had a significant moment of fortune too when he was put down by Murali Vijay at slip off Yadav on 13.
After five overs of pace from each end, India cut to the chase with the introduction of the two spinners who did so much damage in the recent whitewash series win over New Zealand - and they duly began making inroads.
To the first delivery after morning drinks, Cook tried to use the turn from Jadeja into the leg-side, but missed the ball - and then after umpire Chris Gaffaney had given him out lbw, he unaccountably did not call for a review.
India have adopted the decision review system for the first time in this series, and simulation demonstrated the ball was going on to miss leg-stump. By then, though, Cook had walked off.
Ashwin snaked one past Hameed’s forward-defensive edge and into the back pad from round the wicket, turning it just enough to be hitting off-stump.
Hameed did review Kumar Dharmasena’s lbw decision this time, to no avail.
India’s fielding remained slipshod, however, and Root appeared at ease alongside Ben Duckett, who counted two sweeps among three fours in one over off Ashwin.
It was only when the left-hander was caught low at slip by Rahane off Ashwin, from what was therefore the final ball of the morning, that the advantage was with India.
But Root ruled the afternoon, and found an able partner too on his way to and beyond a four-hour hundred which contained nine fours.
Moeen greeted the reintroduction of Ashwin shortly before tea by hitting his first delivery over mid-on for four to bring up the century stand and England’s 200, and soon after the resumption Root dispatched Jadeja’s second ball of a new spell for a memorable straight six.
His hundred was the first by an overseas batsman in India since Michael Clarke in early 2013 - while Ashwin had to get accustomed to the unusual experience of conceding more than 100 runs in a day.
With Shami regularly needing extensive treatment on an apparent hamstring injury, having pulled out mid-over before tea, India were in comparative disarray.
Even after Root’s dismissal, England were still taking their chance to puncture any preconceptions and sow some doubts.
But they must be sure to consolidate on day two, because their arduous task has barely begun yet.